sequences in n- sumf(r)

[Jim Nastos]

On Sun, 30 Nov 2003, murthy amarnath wrote:

> Largest prime in the sequence n- sum f(r) where
>  sum f(r)= f(1) +f(2) ...f(r).
> 0 if no such prime exists.
> Seq(1): e.g. f(r) = r(r+1)/2 = r'th triangular number.
> a(30) = 3,
> we have ----> 30, 29, 28, 25,21,16,10, and finally 3.
> a(36) = 0. ---> 36,35,33,30,26,21,15,8,0.

  I really don't think you are being consistent here... The second 
"sequence" used for calculating a(36) (these should only be called sets, 
since you are not requiring any order on these numbers) is {36, (36-1), 
(36-3), (36-6), (36-10), (36-15), (36-21), (36-28), (36-36)} which is just 
n-T(i), where T(i) is the i(th) triangular number... where are you taking 
sum(T(i)) ?
  This is not consistent with your first "sequence" used for a(30) where 
you have {30, (30-1), (30-2), (30-5), (30-9), (30-15), (30-20), (30-27)}. 
I can't figure out what 1, 2, 5, 9, 15, 20, 27 have to do with the 
triangular number.
  And if you are letting f(r) = r(r+1)/2, I don't see any sum(f(r)) 
anywhere.

> I have conjectured that there are finitely many zeros
> in this sequence (A090302).

  I can't find this sequence in the database, so I can't see another 
example of what you are trying to say. Please be more precise because 
I'd like to know exactly what idea you have here.

J